Abstract
We study the computational complexity of Boolean constraint satisfaction problems with cardinality constraint. A Galois connection between clones and co-clones has received a lot of attention in the context of complexity considerations for constraint satisfaction problems. This connection fails when considering constraint satisfaction problems that support in addition a cardinality constraint. We prove that a similar Galois connection, involving a weaker closure operator and partial polymorphisms, can be applied to such problems. Thus, we establish dichotomies for the decision as well as for the counting problems in Schaefer’s framework.
Supported by the DAAD postdoc program. Work done in part while the second and third authors worked at the University of Hannover.
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Creignou, N., Schnoor, H., Schnoor, I. (2008). Non-uniform Boolean Constraint Satisfaction Problems with Cardinality Constraint. In: Kaminski, M., Martini, S. (eds) Computer Science Logic. CSL 2008. Lecture Notes in Computer Science, vol 5213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87531-4_10
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DOI: https://doi.org/10.1007/978-3-540-87531-4_10
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